Ok. I have a unused desktop and i want to dissect it to put fresher parts in it (it currently runs Pentium 4). Do i really...

Send it in to apple for repairs. More information : http://www.apple.com/batteries/

I think all products are eligible to send it to apple, just that if its under warranty and doesnt fits the you-done-this-so-there-goes-your-warranty kind of action (jailbreaking for one), it would be free. BUT if its out of warranty or if you have tempered with it in such a way that your warranty is voided, i think you need to pay for whatever service you need. hope this helps. Source: Read it somewhere before, didnt remember PS: can go to : http://images.apple.com/legal/warranty/d...

Uh TV i think needs a HDMI cable?

Mine had the same problem... maybe not that serious. Mine was a bit stiff but just trying with each press of the home button apply slightly more pressure on it (it won't break LOL) and hold it for a little longer? That worked for me.

Apple confirmed it at 512MB. Can check Macrumors.com